HOUSTON — Jeffrey Lee Wood is sentenced to die this week for the murder of a store clerk during a robbery, even though he was sitting in a truck outside the convenience store when it happened.

Mr. Wood is the latest person to face the death penalty under a Texas law that makes accomplices subject to the death penalty if a murder occurs during a crime.

His lawyers say Mr. Wood is a gullible man of limited intellect who suffers from delusions. In their view, Mr. Wood was never mentally competent to stand trial in the first place.

Nor, they argue, was Mr. Wood aware that his partner in the robbery, David Reneau, was carrying a gun, according to testimony presented at Mr. Reneau’s trial but never brought up during Mr. Wood’s trial.

These arguments failed to sway the Texas Board of Pardons and Paroles, however. On Tuesday afternoon, the seven-member board unanimously rejected a petition from Mr. Wood’s lawyers for a commutation of his sentence.

Mr. Wood, who is 35, also lost a motion before the Texas Court of Criminal Appeals on Tuesday. His lawyers had asked the court to appoint a lawyer to pursue the argument that Mr. Wood lacks the mental competence to be executed.

Mr. Wood and Mr. Reneau were tried separately for the killing of Kriss Keeran, a 31-year-old cashier who was shot in the forehead during the robbery of a gas station and convenience store in Kerrville, Tex., on Jan. 2, 1996.

Mr. Reneau was executed in 2002.

The two robbers were roommates and knew the victim. Evidence at the two trials showed the pair had planned the robbery for about two weeks and had talks with Mr. Keeran and an assistant manager at the store, William Bunker, about staging a fake robbery.

But that plan went awry, and Mr. Reneau ended up walking into the store and shooting Mr. Keeran between the eyes with a .22-caliber pistol while Mr. Wood waited outside.

Then he and Mr. Wood carried the store safe and the store’s security camera out and retreated to a house belonging to Mr. Wood’s parents, where they tried to break open the safe. At the house, Mr. Wood bragged to a relative about the robbery.

A jury found Mr. Wood incompetent to stand trial after listening to testimony from a psychiatrist who said Mr. Wood was delusional and could not grasp reality. But after Mr. Wood spent a short stint in a mental hospital, a second jury found him competent. The judge did not let Mr. Wood’s lawyers cross-examine some witnesses at that hearing.

After his conviction, Mr. Wood wanted to represent himself in deliberations on his sentence, but the judge refused. Mr. Wood ordered his lawyers not to cross-examine any witnesses in the proceeding, a decision his lawyers at the time called “a gesture of suicide.” The jury voted for the death penalty.

Lucy Wilke, the Kerr County assistant district attorney who prosecuted Mr. Wood, did not return calls from a reporter. After Mr. Wood’s trial in 1988, she said that he was “not a dummy” and that the slaying was “cold-blooded, premeditated.”

Under the Texas “law of parties,” the question of whether Mr. Wood anticipated the murder is important. People who conspire to commit a felony are all responsible for an ensuing crime, like murder, if it can be shown they should have known it would happen.

The United States Supreme Court has upheld the principle, ruling in 1987 that the Constitution does not forbid the death penalty for a defendant “whose participation in a felony that results in murder is major and whose mental state is one of reckless indifference.”

At least seven people have been executed in the United States since 1985 for being accomplices in crimes during which one of their partners committed murder, according to the Death Penalty Information Center. Three of those were executed in Texas.

David R. Dow, a law professor in Houston who oversees the Texas Defenders Project, which is trying to forestall the execution, said he doubted Mr. Wood was mentally competent to stand trial, much less that he knew in advance the murder would happen. In addition, Mr. Dow said, he did not receive proper legal representation during the sentencing phase.

“This case has in it virtually every feature that makes the death penalty system in Texas so scandalous,” he said.